Reduced crosstalk photonic switch

ABSTRACT

Described are various configurations of reduced crosstalk optical switches. Various embodiments can reduce or entirely eliminate crosstalk using a coupler that has a power-splitting ratio that compensates for amplitude imbalance caused by phase modulator attenuation. Some embodiments implement a plurality of phase modulators and couplers as part of a dilated switch network to increase overall bandwidth and further reduce potential for crosstalk.

PRIORITY

This application is a continuation of U.S. application Ser. No.17/161,104, filed Jan. 28, 2021, which is a continuation of U.S.application Ser. No. 16/839,597, filed Apr. 3, 2020, which is acontinuation of U.S. application Ser. No. 16/267,446, filed Feb. 5,2019, which is a continuation of U.S. application Ser. No. 15/920,769,filed Mar. 14, 2018, which is incorporated by reference herein in itsentirety.

TECHNICAL FIELD

The present disclosure generally relates to switches for switchingnetworks, and more particularly to reduced crosstalk optical switches.

BACKGROUND

Some communication networks, such as those used in data centers, routecommunications between devices using a network of switches. In somenetworks, the switches are Mach-Zehnder optical switches that use phasemodulators and couplers, adjust the phase modulators' state to selectwhich switch input and output ports are connected, and route lightcarrying signals to end devices (e.g., client device, a server). AMach-Zehnder optical switch can split incoming light into componentsrouted down multiple paths. The Mach-Zehnder optical switch then usesone or more phase modulators to create constructive or deconstructiveinterference in an output coupler at the potential output paths in orderto select where the light is routed. Crosstalk between different lightbeams traversing the network of switches can arise due to the physicalcharacteristics of the couplers and phase modulators, and can increaseas light passes through successive switching nodes. Further, currentapproaches for reducing crosstalk, e.g., low-attenuation thermalswitches, are power-hungry and cannot be implemented in networkarchitectures that have a large number of switches, such as a modernoptical switch network.

BRIEF DESCRIPTION OF THE DRAWINGS

To easily identify the discussion of any particular element or act, themost significant digit or digits in a reference number refer to thefigure (“FIG.”) number in which that element or act is first introduced.

FIG. 1 shows a network architecture implementing reduced crosstalkswitches, according to some example embodiments.

FIG. 2 shows a Mach-Zehnder Interferometer (MZI) reduced crosstalkswitch, according to some example embodiments.

FIG. 3 shows a response graph of a multiple quantum well (MQW)modulator, according to some example embodiments.

FIG. 4 shows a coupler that can be integrated into an optical switch tocompensate for phase-modulator-based attenuation, according to someexample embodiments.

FIG. 5 shows a switch architecture with two couplers, according to someexample embodiments.

FIG. 6 shows a flow diagram of a method for routing light through areduced crosstalk switch, according to some example embodiments.

FIG. 7 shows a flow diagram of a method for fabricating apower-efficient reduced crosstalk optical switch, according to someexample embodiments.

FIG. 8 shows a dilated switch that can be used to reduce crosstalk,according to some example embodiments.

DETAILED DESCRIPTION

The description that follows includes systems, methods, techniques, andinstruction sequences that embody illustrative embodiments of thedisclosure. In the following description, for the purposes ofexplanation, numerous specific details are set forth in order to providean understanding of various embodiments of the inventive subject matter.It will be evident, however, to those skilled in the art, thatembodiments of the inventive subject matter may be practiced withoutthese specific details. In general, well-known instruction instances,protocols, structures, and techniques are not necessarily shown indetail.

An optical packet switch is a reconfigurable, low-latency opticalrouting network component used in some data communication networks. Someswitch networks (e.g., using Benes or Banyan architectures) can beimplemented using photonic integrated circuit (PIC) technology. Oneexample of a switch component used within a switch network is a 2×2 MachZehnder Interferometer (MZI), which uses a coupler to split an incominglight beam into multiple beams, each directed down different paths. Oneor more phase modulators are used to create phase differences betweenthe beams on the different paths. A second coupler is used to interferethe beams on multiple paths and couple the beams to output ports. Thephase differences cause constructive and destructive interference atseveral possible output paths, determining to which path the signal isrouted. A 2×2 MZI has two input and two output ports, and uses one ormore phase modulators to switch between its “cross” and “bar”transmission states.

Generally, the radix count (quantity of ports) of a switch network islimited by the crosstalk, insertion loss, and power consumption of theimplemented switches. Further, the total crosstalk and insertion lossfor a given switch network can be calculated from summing contributionsfrom all the components in an optical path through the switch network.As a component in an optical packet switch, an MZI has quantifiablecrosstalk and insertion loss.

Herein, when referring to an individual switch, crosstalk is the ratioof the power of light beams exiting two output ports, where the lightbeams originates at a single input port. One of the output ports is theintended path. The switch is configured such that the port of theintended path is a constructive port of the output coupler, and thesecond output port is a destructive port of the output coupler. Further,in the context of switch networks that include multiple light beams andmultiple switches along an optical path, crosstalk is the ratio of thepower of a light beam at an output port or along an optical path to thetotal power of another light beam at the same location in the switchnetwork due to individual switches' crosstalk.

Crosstalk can stem from several potential sources within a given switch.Some sources include couplers with mistargeted splitting ratios, andwaveguides fabricated with insufficient tolerances that cause randomvariations in insertion loss or optical path length. An additionalsource of crosstalk includes amplitude change caused by phase modulatorelements. In silicon photonics modulators using carrier plasmamodulation, a change in phase is accompanied by a change in insertionloss. The change in insertion loss causes an amplitude imbalance inlight beams that interfere at the output coupler of the MZI, which leadsto crosstalk. Silicon modulators based on the carrier plasma dispersioneffect can operate at frequencies in the GHz range and can be used inoptical packet switches. Fast modulation in PICs can also beaccomplished by modulators that use the quantum-confined Stark effect orthe Franz-Keldysh effect; however, these suffer the same amplitudeimbalance issue when used in switches. The amplitude imbalance puts alower limit on the attainable crosstalk in a switching element, andfurther limits the size of the overall packet switch.

While some thermal phase modulators exhibit little to no amplitudeimbalance, thermal phase modulators have high power consumption and haveslow rise/fall times (e.g., a microsecond), thus limiting theirusefulness in packet switching.

To this end, an improved switch that is specially configured to optimizethe split ratios of a coupler can be implemented to cancel out crosstalkdue to amplitude imbalance caused by absorption from the switch's phasemodulator. In some embodiments, light that has been phase shifted fromthe phase modulators is input into a multimode interference component(MMI), such as a 2×2 MMI. The MMI is fabricated with tapered sides suchthat the power splitting ratio compensates for amplitude imbalance. Theconfigured power splitting ratio results in perfect or near-perfectdeconstructive interference on one output of a 2×2 MMI. The improvedswitch can be integrated into high-radix count switch networks toeliminate crosstalk between different light beams traversing thenetwork.

Herein, the term beam is interpreted electromagnetic waves (e.g., light,optical signal) that can travel down a channel (e.g., waveguide, a fiberoptic cable). Beams can be coded to carry one or more signals, e.g.,data streams. Beams can be separated (e.g., split) into components. Thecomponents of a beam are in themselves beams, each of which may includeone or more signals of the original beam. Unless specified, routing,splitting, phase shifting or otherwise modifying is a manipulation ofthe beam itself, not the underlying one or more signals that a givenbeam may carry. For example, if a beam is split into two componentbeams, each of the two component beams may include all signals in theoriginal beam or a portion of the signals in the original beam.

FIG. 1 shows an example network architecture 100 implementing reducedcrosstalk switches, according to some example embodiments. The networkarchitecture 100 comprises a plurality of endpoints 105A-105F devices(e.g., computers such as a laptop, desktop, or server in a datacenter)that send light data back and forth over an optical switch network 110.The optical switch network 110 comprises a plurality of switches115A-115D that route light carrying signals between the plurality ofendpoints 105A-105F. For example, as shown in FIG. 1., endpoint device105C (a tablet) and endpoint device 105E (a datacenter) are transmittinginformation via switch 115C and switch 115B, as illustrated by thedashed-arrows between the endpoints.

Although only four switches 115A-115D are illustrated in FIG. 1, theoptical switch network 110 can include a multitude of switches toincrease the overall bandwidth of the network 110. Further, each switchmay comprise multiple sub-component switches as part of a dilatedswitch, as discussed in further detail below. The plurality of switches115A-115D can simultaneously route multiple light carrying signalsbetween the plurality of endpoints 105A-105F. As discussed, one possiblesource of crosstalk is an amplitude imbalance within a switch leading toincomplete destructive interference, causing noise on a “victim” signaldue to unintended crosstalk from an “aggressor” signal. For instance a2×2 MZI switch operating in the “bar” state may have a small fraction oflight passing through the “cross” state. In some example embodiments,one or more of the plurality of switches 115A-115D have phase modulatorsand MMI couplers that are configured to cancel out amplitude imbalancescaused by the phase modulators. Eliminating amplitude imbalance in apower-efficient way reduces crosstalk in the optical switch network 110,thereby allowing the optical switch network 110 to integrate moreswitches and route larger amounts of information between a larger numberof endpoints.

FIG. 2 shows an example reduced crosstalk switch 200, according to someexample embodiments. The switch 200 is configured as a 1×2 Mach-ZehnderInterferometer (MZI) switch that uses symmetric couplers, with threeports: A, B, and C. Although the switch 200 can operate in eitherdirection (i.e., light is input into the 1×2 coupler 205 and output at2×2 coupler 220, or vice versa), the below discussion assumes lighttraverses the switch 200 from left to right (i.e., light is input intoport A and emanates from ports B and/or C).

As illustrated in FIG. 2, a 1×2 coupler 205 has one input port (port A)and two output ports (unlabeled ports connected to phase modulators 210and 215). In some example embodiments, the 1×2 coupler 205 is a 1×2 MMIor waveguide Y-junction. Each of the output ports of 1×2 coupler 205outputs to respective phase modulators, phase modulator 210 and phasemodulator 215. The phase modulators 210 and 215 output to a 2×2 coupler220, which has two input ports and two output ports. In some exampleembodiments, the 2×2 coupler 220 is a 2×2 MMI. The dotted linesconnecting the respective components of the architecture of switch 200are channels for light data, e.g., waveguides, fiber optics.

With reference to FIG. 2, a “phase arm” refers to components that makeup a path along the top or bottom of switch 200 between optical couplers205 and 220.

The phase modulators 210 and 215 can have phase shifts adjusted todetermine whether all the light entering (or exiting) port A exits (orenters) via port B, whether a fraction of light exits (or enters) bothports B and C, or whether all light from port A exits (or enters) viaport C. In some example embodiments, a light beam is input into port Aof the 1×2 coupler 205 and is symmetrically split into a top output andbottom output of 1×2 coupler 205. Each of the output beams of 1×2coupler 205 have identical phases and 50% of the original power (e.g.,50% power of the light input into port A). The phase modulators 210 and215 can phase shift the light such that when the light is coupled in the2×2 coupler 220, the difference in phases causes deconstructiveinterference at one output port of the 2×2 coupler 220 and constructiveinterference at the other output port.

In some example embodiments, the switch 200 operates in two states,where in each state, only one of the phase modulators is turned on. In afirst state, phase modulator 215 is turned on and has a phase shift,applied to the light, of π/2, and phase modulator 210 is off and haszero phase shift. In the first state, all the light input into switch200 exits the top output B of switch 200 due to the two beamsconstructively interfering at port B and destructively interfering atport C. In a second state, phase modulator 215 is off and has zero phaseshift while phase modulator 210 is turned on and has π/2 phase shift. Inthe second state, all the light input into switch 200 exits port C dueto the signals constructively interfering at port C and destructivelyinterfering at port B.

If the amplitudes of the components of the light entering the two inputsof the 2×2 coupler 220 are the same, then for the correct phase shiftperfect deconstructive interference occurs in the port B or C for whichno light is intended to exit. However, if the amplitudes of the twocomponents of the light entering the two inputs of the 2×2 coupler 220are not the same, complete destructive interference will not occur,leading to crosstalk. Further, some phase modulators with desirablecharacteristics (e.g., power efficient, GHz response times) have anabsorption of the light being phase shifted that varies with the amountof phase shift, thereby causing amplitude imbalance in the 2×2 coupler220 and crosstalk.

FIG. 3 shows an example response graph 300 of a multiple quantum well(MQW) modulator, according to some example embodiments. Multiple quantumwell (MQW) modulators modulate the phase and amplitude of light bychanging the complex refractive index of the modulator by changing anapplied electric field. As illustrated, as the MQW modulatorincreasingly shifts the phase of light, the amplitude of the light isincreasingly attenuated. Returning to FIG. 2, thus if phase modulator210 is a MQW modulator and turned on with a π/2 phase shift, theamplitude of the phase-shifted light will be lower than thenon-phase-shifted light being passed through phase modulator 215.

In some example embodiments, light traversing the switch 200 can bemodeled using transfer matrices. A column vector is shown in Expression1:

$\begin{matrix}\begin{bmatrix}1 \\j\end{bmatrix} & {{Ex}.1}\end{matrix}$

Expression 1 represents the amplitudes and relative phases of light inthe waveguide modes at a cross-section along the switch 200, or at theinput or output of a coupler. In some example embodiments, the number ofelements of the column vector is the same as the number of waveguides atthat cross-section, and each waveguide is assumed to carry light in onlya fundamental mode.

The 1×2 coupler 205 can be modeled as a transfer matrix that splits aninput mode (e.g., light input into 1×2 coupler 205) into two modeshaving the same phase, as will occur in a 1×2 MMI or a waveguideY-junction. In some example embodiments, the input of the 1×2 coupler205 is as follows:

$\begin{matrix}{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}} & {{Ex}.2}\end{matrix}$

If operating on an input field distribution to create an output fielddistribution, the output field (e.g., two modes in two waveguides) is afunction of the input field (e.g., one mode in one waveguide). That is:

$\begin{matrix}{\begin{bmatrix}E_{out}^{1} \\E_{out}^{2}\end{bmatrix} = {{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}}\left\lbrack E_{in}^{1} \right\rbrack}} & {{Ex}.3}\end{matrix}$

As is appreciated by one of ordinary skill in the art, Kramers-Kroniganalysis can yield expressions for change in absorption and phase as afunction of carrier density in silicon. Applied here, operating at 1310nm: (1) dn=−7.7625 e−023*N{circumflex over ( )}1.05−4.7863e−018*P{circumflex over ( )}0.805; and (2) dabs (1/cm)=1.7925E−20*N.{circumflex over ( )}1.14+5.9858 E−20* P.{circumflex over( )}1.1. N and P represent electron and hole densities per cm³.

The phase modulator arms can be set to use two operating states whichhave phase shifts of (0, π/2) and (π/2, 0). The field transmissioncoefficient of a modulator with π/2 phase shift, relative to that of amodulator with zero phase shift, will be given by t. For the twooperating states, the transfer matrix of the phase modulator arms willbe:

$\begin{matrix}{\begin{bmatrix}1 & 0 \\0 & {jt}\end{bmatrix},\begin{bmatrix}{jt} & 0 \\0 & 1\end{bmatrix}} & {{Ex}.4}\end{matrix}$

Where, in Expression 4:

j=√{square root over (−1)}=e ^(jπ/b)  Ex. 5

The transfer matrix of the output 2×2 coupler 220, if implemented withan MMI using a 50% splitting ratio, is as follows:

$\begin{matrix}{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- j} \\{- j} & 1\end{bmatrix}} & {{Ex}.6}\end{matrix}$

The transfer matrices of a switch in the two operating states for lightentering the left side (into 1×2 coupler 205) are as follows:

$\begin{matrix}{{{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- j} \\{- j} & 1\end{bmatrix}}\begin{bmatrix}1 & 0 \\0 & {jt}\end{bmatrix}}{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\2\end{bmatrix}}},{{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- j} \\{- j} & 1\end{bmatrix}}\begin{bmatrix}{jt} & 0 \\0 & 1\end{bmatrix}}{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}}}} & {{Ex}.7}\end{matrix}$

Expression 7 can be simplified to:

$\begin{matrix}{{\frac{1}{2}\begin{bmatrix}{1 + t} \\{{jt} - j}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}{{jt} - j} \\{1 + t}\end{bmatrix}}} & {{Ex}.8}\end{matrix}$

If there is no loss, then t=1 and the expressions simplify to:

$\begin{bmatrix}1 \\0\end{bmatrix},{\begin{bmatrix}0 \\1\end{bmatrix}.}$

With loss, the crosstalk (in dB) in both switch states is as follows:

$\begin{matrix}{20*\log 10\left( \frac{1 + t}{1 - t} \right)} & {{Ex}.9}\end{matrix}$

As described with light entering the switch 200 through the side with asingle port (i.e., into port A), the switch will be configured such thatone of the two output ports (e.g., port B, port C) is the intendedoutput port and the constructive port, and any light exiting thedestructive port causes crosstalk. If the switch 200 is operated in theopposite direction with two distinct light beams entering the two portson the same side (i.e., port B and C), only one of the two signals willbe intentionally passed to the single port (i.e., port A) on theopposite side. Any portion of the other light beam exiting the singleport on the opposite side will cause crosstalk.

In some example embodiments, the phase modulators (e.g., phasemodulators 210 and 215) are based on the carrier plasma dispersioneffect and can modulate light by changing the complex refractive indexof the modulator based on quantities of charge carriers (e.g., N and P)injected into the semiconductor material of the modulator. If phasemodulators 210 and 215 are carrier-plasma-dispersion-based modulators,when operating at 1310 nm, and if phase modulator 210 and phasemodulator 215 are each 100 microns long, carriers are injected into thephase modulators 210, 215 so that the N and P concentrations are ˜1.7E18/cm 3, which yields a shift of π/2 in one arm, while the other arm isin an off-state, according to some example embodiments. The resultingfield transmission of t is then 0.916, with an insertion loss of 0.77 dBin the modulating phase arm. Further, the crosstalk in thisconfiguration is 27.1 dB.

The crosstalk of the architecture 100 of switch 200 can be eliminated ifthe power splitting ratio of the 2×2 coupler 220 is speciallyconfigured. For a rectangular 2×2 coupler, also known as a multimodeinterferometer (MMI), several power splitting ratios can be obtained, asis appreciated by those of ordinary skill in the art:

$\begin{matrix}{\frac{P_{c}}{P_{b}} \cong \left\{ {\frac{50}{50},\frac{100}{0},\frac{85}{15},\frac{72}{28}} \right\}} & {{Ex}.10}\end{matrix}$

where P_(c) is the power output of one output port of the 2×2 coupler220, and P_(b) is the power output from the other port of the 2×2coupler 220.

According to some example embodiments, while some phase modulators (suchas MQW modulators or carrier-plasma-dispersion effect-based phasemodulators) are power efficient, they can cause attenuation in thephase-shifted light, causing an amplitude imbalance between channelsentering a coupler in which light in the channels undergoesinterference, and subsequent crosstalk at the output of the coupler.Making matters worse, modern optical switching networks require a largenumber of successive switch stages, thereby increasing the potential forcrosstalk. Crosstalk in such a network cannot simply be fixed byimplementing phase modulators that do not attenuate (such asthermal-based phase modulators). This is due to low-attenuation phasemodulators requiring appreciable amounts of power to operate, andimplementing those phase modulators in a high radix count network wouldresult in a power-hungry, commercially impractical architecture.

FIG. 4 shows an example coupler 400 that can be integrated into anoptical switch to compensate for phase modulator-based attenuation,according to some example embodiments. Coupler 400 is a 2×2 opticalcoupler with a length L and width W0, and two inputs and outputs,including input A, output A, input B, and output B. Generally, coherentlight can be input into input A and/or input B, mix or interfere, andemanate from output A and/or output B depending on the phase differencesand amplitudes of the inputs. For example, if the light entering inputsA and B are of the same amplitude but there is a difference in phase ofπ/2, then constructive interference may occur for output A, whichrepresents a high-signal, whereas deconstructive interference may occurfor output B, representing low-signal. By controlling the relativephases of the light at the two inputs to the coupler, the input lightcan be routed to one output or the other.

As illustrated, the coupler 400 has a tapered midsection, with both itssides offset (e.g., indented) from the sides of a rectangle coupler by adistance 51 dW|. Further, the coupler 400 has a gap 405 of width W1. Thetapered sides and gap 405 of coupler 400 can be configured to vary thepower splitting ratio of the coupler 400 due to path differences oflight in superposition in the coupler 400. In particular, the normalizedpower “P_(a)” of output A may be:

P _(c)=cos(0,5·πdΩ)²  Ex. 11

where dΩ is normalized width variation. The normalized power of theother output “P_(b)” is then: P_(b)=1−P_(c). Further, the normalizedwidth variation, dΩ, depends on the width of the input face of coupler400, W₀, and the taper, dW:

$\begin{matrix}{{d\Omega} = {{- \left( \frac{dW}{{dW}_{0}} \right)} - \frac{1}{2}}} & {{Ex}.12}\end{matrix}$

In some example embodiments, the splitting ratio can be configured tocompensate for loss in phase arms which may be connected to the coupler.The cross power splitting ratio, S, of the 2×2 coupler 220 may beconfigured as given in Expression 13, in which the field transmission trefers to the ratio of the field transmission coefficient of a phasemodulator with π/2 phase shift to that of a phase modulator with zerophase shift:

$\begin{matrix}{S = \frac{t^{2}}{1 + t^{2}}} & {{Ex}.13}\end{matrix}$

Expression 13 leads to a transfer matrix of the 2×2 coupler 220 asfollows:

$\begin{matrix}{\frac{1}{\sqrt{1 + t^{2}}}\begin{bmatrix}1 & {- {jt}} \\{- {jt}} & 1\end{bmatrix}} & {{Ex}.14}\end{matrix}$

In some example embodiments, in a first switch state, the phasemodulator 210 has a phase shift of π/2, whereas the phase modulator 215has a phase shift of zero (e.g., an off-state). In a second switchstate, the phase modulator 210 is in an off-state, and the phasemodulator 215 has a phase shift of π/2. The transfer matrix of theswitch 200 in the two switch states simplifies to these expressions inwhich all of the transmitted light exits only one port, so that therewill be no crosstalk

$\begin{matrix}{{\sqrt{\frac{1 + t^{2}}{2}}\begin{bmatrix}1 \\0\end{bmatrix}},{\sqrt{\frac{1 + t^{2}}{2}}\begin{bmatrix}0 \\1\end{bmatrix}}} & {{Ex}.15}\end{matrix}$

If operated in the reverse direction, e.g., as a 2×1 coupler, thetransfer matrices in the two switch states are:

$\begin{matrix}{{{{\frac{1}{\sqrt{2}}\left\lbrack {11} \right\rbrack}\begin{bmatrix}1 & 0 \\0 & {jt}\end{bmatrix}}{\frac{1}{\sqrt{\left( {1 + t^{2}} \right)}}\begin{bmatrix}1 & {- {jt}} \\{- {jt}} & 1\end{bmatrix}}},{{{\frac{1}{\sqrt{2}}\left\lbrack {11} \right\rbrack}\begin{bmatrix}{jt} & 0 \\0 & 1\end{bmatrix}}{\frac{1}{\sqrt{\left( {1 + t^{2}} \right)}}\begin{bmatrix}1 & {- {jt}} \\{- {jt}} & 1\end{bmatrix}}}} & {{Ex}.16}\end{matrix}$

Expression 16 simplifies as follows, showing that there is no crosstalkwhen operating as a 2×1 coupler:

$\begin{matrix}{{\sqrt{\frac{1 + t^{2}}{2}}\left\lbrack {10} \right\rbrack},{\sqrt{\frac{1 + t^{2}}{2}}\left\lbrack {01} \right\rbrack}} & {{Ex}.17}\end{matrix}$

In some example embodiments, the switch 200 may only have 1 phasemodulator. That is, two beam components are output from 1×2 coupler 205,and one of the beam components is input into the only phase modulator(e.g., phase modulator 210) in switch 200, and the beams are coupled in2×2 coupler 220 to compensate for phase modulator caused imbalance. Insome embodiments only having one phase modulator, the beam componentsoutput from 1×2 coupler 205 will have an uneven splitting ratio.

FIG. 5 shows a switch 500 with two 2×2 couplers 505, 520, according tosome example embodiments. In switch 500, two light beams are input intoa 2×2 coupler 505 (e.g., one light beam is input into port A, anotherlight beam is input into port B). The 2×2 coupler 505 outouts into twophase modulators 510 and 515. The two phase modulators 510 and 515output into another 2×2 coupler 520. In FIG. 5, a “phase arm” refers tocomponents that make up a path along the top or bottom of switch 500between 2×2 couplers 505 and 520.

In switch 500, if both the bottom and top phase arms are of the samelength and both phase arms are in an off state (e.g., phase modulators510 and 515 are off), there is perfect cross coupling if the sum of thesplit ratios of the two couplers is 100%. However, when switch 500 ismanufactured, fabrication imperfections can arise that lead to amplitudeimbalance and crosstalk. In some embodiments, one or more of thecouplers of switch 500 can be tuned by varying the coupling ratio tocompensate for fabrication imperfections. In some example embodiments,this tuning can be achieved using the coupler with a tapered midsectionshown in FIG. 4. In particular, for example, 2×2 coupler 520 can betuned to create a cross power splitting ratio given by the followingexpression, in which t is the ratio of field transmission coefficientsfrom a phase modulator with n phase shift to that of a phase modulatorwith zero phase shift:

$\begin{matrix}{S = \frac{t}{1 + t}} & {{Ex}.18}\end{matrix}$

Couplers with cross power splitting ratios S & 1−S can exhibit transfermatrices as follows:

$\begin{matrix}{{\frac{1}{\sqrt{1 + t}}\begin{bmatrix}1 & {{- j}\sqrt{t}} \\{{- j}\sqrt{t}} & 1\end{bmatrix}},{\frac{1}{\sqrt{1 + t}}\begin{bmatrix}\sqrt{t} & {- j} \\{- j} & \sqrt{t}\end{bmatrix}}} & {{Ex}.19}\end{matrix}$

With the couplers 505 and 520 placed in series, separated by a losslesspair of equal length phase arms expressed by the matrix

$\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix},$

the transfer matrix of the resulting switch 500 is that of a cross statewith no crosstalk, independent of field transmission value of t, where tis assumed to be a non-negative real number,

$- {{j\begin{bmatrix}0 & 1 \\1 & 0\end{bmatrix}}.}$

If one of the phase arms is modulated so that the phase shifts betweenthe arms are separated by 180° (e.g., (0,π)), and if the ratio of fieldtransmission of the modulated arm at 180° phase shift to that with themodulated arm at 0° phase shift is t, the transfer matrix of the phasesection will be:

$\begin{bmatrix}1 & 0 \\0 & {- t}\end{bmatrix}.$

Further, the transmission of the switch 500 is then:

$\begin{matrix}{{{\frac{1}{\sqrt{1 + t}}\begin{bmatrix}1 & {{- j}\sqrt{t}} \\{{- j}\sqrt{t}} & 1\end{bmatrix}}\begin{bmatrix}1 & 0 \\0 & {- t}\end{bmatrix}}{\frac{1}{\sqrt{1 + t}}\begin{bmatrix}\sqrt{t} & {- j} \\{- j} & \sqrt{t}\end{bmatrix}}} & {{Ex}.20}\end{matrix}$

Expression 20 simplifies to:

$\begin{matrix}{\frac{1}{1 + t}\begin{bmatrix}{\sqrt{t}\left( {1 + t} \right)} & {j\left( {t^{2} - 1} \right)} \\0 & {{- \sqrt{t}}\left( {1 + t} \right)}\end{bmatrix}} & {{Ex}.21}\end{matrix}$

If input modes are

${\begin{bmatrix}1 \\0\end{bmatrix}{{and}\begin{bmatrix}0 \\1\end{bmatrix}}},$

the output modes are

${\begin{bmatrix}\sqrt{t} \\0\end{bmatrix}{and}} - {\begin{bmatrix}{j\left( {1 - t} \right)} \\\sqrt{t}\end{bmatrix}.}$

For the first mode,

$\begin{bmatrix}1 \\0\end{bmatrix},$

there is no crosstalk. It is possible to avoid crosstalk from the secondmode

$\begin{bmatrix}0 \\1\end{bmatrix}$

if the other arm in the phase section is modulated to a 180° phase shiftwith field transmission of t, expressed by transfer matrix

$\begin{bmatrix}1 & 0 \\0 & {- t}\end{bmatrix}.$

In this case the transmission of the switch 500 is then:

$\begin{matrix}{\frac{1}{1 + t}\begin{bmatrix}{{- \sqrt{t}}\left( {1 + t} \right)} & 0 \\{j\left( {t^{2} - 1} \right)} & {\sqrt{t}\left( {1 + t} \right)}\end{bmatrix}} & {{Ex}.22}\end{matrix}$

If the switch is operated in the reverse direction (e.g., lighttraverses from 2×2 coupler 520, through phase modulators 510 and 515,and is output from 2×2 coupler 505), the first state of the phasesection is expressed as

$\begin{bmatrix}1 & 0 \\0 & {- t}\end{bmatrix},$

and the transmission of the switch 500 is as follows:

$\begin{matrix}{\frac{1}{1 + t}\begin{bmatrix}{\sqrt{t}\left( {1 + t} \right)} & 0 \\{j\left( {t^{2} - 1} \right)} & {{- \sqrt{t}}\left( {1 + t} \right)}\end{bmatrix}} & {{Ex}.23}\end{matrix}$

In the reverse direction embodiment, light entering switch 500 in thereverse direction in mode

$\begin{bmatrix}0 \\1\end{bmatrix}$

will have no crosstalk.

According to some example embodiments, switch 500 can operate in threedifferent states: a passive cross state, a first bar state, and a secondbar state. In some example embodiments, configuring switch 500 tooperate in one of the three states may be useful in networkarchitectures in which not all possible paths are carrying signals atthe same time. In the following discussion, A→D can be interpreted as alight beam traversing from port A to port D across the entire switch 500(e.g., through superposition in couplers 505 and 520, etc.)

In the passive cross state, light can traverse from A→D or from D→A.Similarly, light can traverse from B→C and from C→B. In the cross state,both phase modulators 510 and 515 are in an off state and crosstalk doesnot occur.

In the first bar state, phase modulator 510 operates at a 180° phaseshift, phase modulator 515 is off, and field transmission is t: a barstate. In the first bar state, light traversing C→A and B→D does nothave crosstalk. On the other hand, light traversing A→C and D→B exhibitscrosstalk due to imbalance.

In the second bar state, phase modulator 515 operates at 180° phaseshift, phase modulator 510 is off, and field transmission is t: barstate. In the second bar state, light traversing A→C and D→B does nothave crosstalk. On the other hand, light traversing C→A and B→D exhibitscrosstalk due to imbalance.

In either first and second bar states, the crosstalk in dB is:

$\begin{matrix}{20*\log 10\left( \frac{\sqrt{t}}{1 - t} \right)} & {{Ex}.24}\end{matrix}$

This is an improvement over approaches implementing 50% couplers (i.e.,instead of split ratios S & 1−S), where the crosstalk for all inputstates is higher regardless of which arms are modulated:

$\begin{matrix}{20*\log 10\left( \frac{1 + t}{1 - t} \right)} & {{Ex}.25}\end{matrix}$

In some example embodiments, phase modulators 510 and 515 arecarrier-injection-based modulators 150 microns in length. In thoseembodiments, to implement a 180-degree phase shift, carriers areinjected so that the N and P concentrations are ˜2.3 E18/cm 3, whichresults in a field transmission of t=0.830, and insertion loss of 1.61dB in the modulating phase arm. If couplers 505 and 520 are 50%couplers, the crosstalk in the bar state for both inputs is 20.7 dB.

In some example embodiments, couplers 505 and 520 use power splittingratios of 1/(1+t) and t/(1+t) respectively. In those embodiments, one orboth of phase modulators 510, 515 can be tapered to compensate forimbalance, as discussed above. In those embodiments, in one directionthere will be optimally zero crosstalk, while in the other directioncrosstalk of 14.6 dB can occur.

In some example embodiments, the 2×2 switch 500 is configured as a 1×2switch by removing one of the ports and one of the phase modulators.Control of the modified 2×2 switch architecture is simplified comparedto switch architecture 200 (a 1×2 switch embodiment) because there isone less phase modulator to manage. In these example embodiments, alight beam traversing the path in which the phase modulator was removedmay traverse from the initial coupler (e.g., coupler 505) to the othercoupler (e.g., coupler 520) via a passive optical waveguide withouttraversing a phase modulator.

FIG. 6 shows a flow diagram of a method 600 for routing light through areduced crosstalk switch, according to some example embodiments. In someexample embodiments, a single switch (e.g., switch 200, switch 500)implements method 600, while in some example embodiments a switchnetwork (e.g., dilated switch 800 of FIG. 8, discussed below) implementsmethod 600.

At operation 605, a coupler receives light, e.g., one or more beams oflight. For example, with reference to FIG. 5, coupler 505 receives afirst beam at port A and a second beam at port B. At operation 610, thecoupler 605 routes the one or more received beams of light onto multiplephase arms. For example, with reference to FIG. 5, 2×2 coupler outputslight onto a top phase arm and bottom phase arm of switch 500, asdiscussed above.

At operation 615, light on the phase arms is phase-shifted using one ormore phase modulators. For example, phase modulator 510 is acarrier-injection-based phase shifter configured to phase-shift light onthe top phase arm by π/2, as discussed above. Further, in some exampleembodiments, while phase modulator 510 is configured to impart aphase-shift, phase modulator 515 is in an off state and light on thebottom phase arm retains its initial phase. At operation 220, the lighton the top and bottom phase arms are combined in a second coupler thathas been configured to compensate for attenuation caused by modulation.Continuing the example, if phase modulator 510 is acarrier-injection-based phase modulator, the modulated light on the topphase arm may be attenuated relative to the light on the bottom phasearm. To compensate for the attenuation, the second coupler has asplitting ratio, (e.g., t²/(1+t²)) that compensates for the attenuationin the light on the top phase arm. At operation 625, the second couplertransmits a low-crosstalk output at one or more output ports. Forexample, if the second coupler has two output ports, due to attenuationcompensation, complete destructive interference may occur for one outputport and complete constructive interference may occur for one of theoutput ports.

FIG. 7 shows a flow diagram of a method 700 for fabricating apower-efficient reduced crosstalk optical switch, according to someexample embodiments. At operation 705, a phase modulator phase-shiftslight. At operation 710, the modulated light is analyzed to determine anamount of attenuation caused by the phase modulator. At operation 715,an initial split ratio for a coupler is selected. For example, if thecoupler is a rectangular coupler, a split ratio of P_(c)/P_(b)=50/50 isselected from the possible split ratios (see Expression 10, above). Atoperation 720, the coupler is shaped to minimize crosstalk. For example,if the coupler is a rectangular coupler, the midsection of the couplercan be increasingly tapered by a distance |dW| until the initial splitratio becomes the split ratio (e.g., t²/(1+t²)). In some exampleembodiments, which split ratio is selected and increasingly modifieddepends on different design considerations, including, for example:optical beam strengths, radix count, phase modulator type, amount ofattenuation.

FIG. 8 shows an example dilated switch 800 that can be used to reducecrosstalk, according to some example embodiments. As illustrated,dilated switch 800 comprises multiple switch sub-components 805A-805D,each of which is an individual switch, such as switch 200 or 500.Dilated switch 800 can lower or eliminate crosstalk by ensuring thatonly one light beam carrying signal traverses any of the sub-switchcomponents at once. To that end, as the radix count is increased,additional sub-component switches can be added to dilate the overallswitch architecture and reduce or eliminate potential for crosstalk. Insome example embodiments, to maintain efficient power consumption as theradix count and sub-switch count are increased, one or more of thesub-switches implement carrier-injection-based phase modulators andshaped couplers as explained above. In this way, optical switch network110 can increase its port count and subsequent bandwidth while beingpower efficient and keeping crosstalk low.

What is claimed is:
 1. A method for propagating light using an opticalswitch, the method comprising: receiving a first light and a secondlight using one or more waveguides of the optical switch, the firstlight at a first optical power and a second light at a second opticalpower that is lower than the first optical power due to attenuation, theoptical switch having a physical shape that compensates for theattenuation; forming compensated light using the physical shape of theoptical switch; and transmitting the compensated light to one of aplurality of ports in the optical switch.
 2. The method of claim 1,further comprising: receiving an input light using one or more inputports of the optical switch.
 3. The method of claim 2, furthercomprising: separating the input light into the first light and thesecond light.
 4. The method of claim 3, wherein the input light isseparated into the first light and the second light by a coupler.
 5. Themethod of claim 1, wherein the optical switch comprises a coupler thathas the physical shape that compensates for attenuation differences oflight in the coupler.
 6. The method of claim 5, wherein the coupler hastapered sides that modify a superposition of light in the coupler. 7.The method of claim 6, wherein the superposition of light in the coupleris modified by the tapered sides such that a power splitting ratio ofthe coupler compensates for attenuation differences of light in thecoupler.
 8. The method of claim 7, wherein the power splitting ratio ist{circumflex over ( )}2/(1+t{circumflex over ( )}2), where t is a ratioof field transmission coefficients of an optical component in theoptical switch.
 9. The method of claim 7, wherein the power splittingratio is t/(1+t), where t is a ratio of field transmission coefficientsof an optical component in the optical switch.
 10. The method of claim1, wherein the attenuation is due to one or more optical components inthe optical switch.
 11. The method of claim 10, wherein the one or moreoptical components comprise one or more optical modulators.
 12. Themethod of claim 11, further comprising: modulating the second lightusing the one or more optical modulators.
 13. The method of claim 11,wherein the one or more optical modulators include a phase modulatorthat modulates the second light using phase modulation.
 14. The methodof claim 13, wherein modulating the second light comprises shifting,using the phase modulator, a phase of the second light in the opticalswitch by approximately 90 degrees.
 15. The method of claim 13, whereinmodulating the second light comprises shifting, using the phasemodulator, a phase of the second light in the optical switch byapproximately 180 degrees.
 16. The method of claim 13, wherein the oneor more optical modulators modulate the second light based on a quantityof embedded positive and negative carriers in the one or more opticalmodulators.
 17. The method of claim 13, wherein the one or more opticalmodulators include a first modulator and a second modulator, and whereinthe second modulator modulates the second light while the firstmodulator is inactive.
 18. The method of claim 17, wherein the firstmodulator that is inactive passes the first light unmodulated.
 19. Themethod of claim 1, wherein the compensated light is transmitted to theone of the plurality of ports to an optical network.
 20. An opticalswitch comprising: one or more waveguides to receive a first light and asecond light, the first light at a first optical power and a secondlight at a second optical power that is lower than the first opticalpower due to attenuation, the optical switch having a physical shapethat compensates for the attenuation; and one or more ports to outputcompensated light that is formed using the physical shape of the opticalswitch